Practice Flashcards
State the three log laws (same base a).
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All Flashcards in Topic 1.9
Below are all 8 flashcards for this topic. Sign up free to track your progress and get personalized review schedules.
1.9.18 cards
State the three log laws (same base a).
log(xy) = log x + log y; log(x/y) = log x − log y; log(xⁿ) = n log x.
What does logₐ x = y mean in index form?
aʸ = x — 'the power of a that gives x'. Logs and powers are inverse operations.
What is the change-of-base rule?
logₐ x = log x / log a = ln x / ln a (number on top, old base on the bottom).
How do you solve aˣ = b for x?
Take logs both sides: x log a = log b, so x = log b / log a (the doubling-time / half-life move).
How do you solve logₐ N = k?
Rewrite in index form: N = aᵏ. Then check the inside of the log is positive.
What are logₐ 1 and logₐ a?
logₐ 1 = 0 (a⁰ = 1) and logₐ a = 1 (a¹ = a).
Why must you check the domain after solving a log equation?
Logs are only defined for positive inputs; reject any solution that makes the inside ≤ 0, even if the algebra allows it.
Write 2 log P + log Q − log 5 as one logarithm.
log(P²Q / 5) — power law first, then product (add) and quotient (subtract).
Topic 1.9 study notes
Full notes & explanations for Log laws (HL only)
Math AI exam skills
Paper structures, command terms & tips
Want smart review reminders?
Sign up free to track your progress. Our spaced repetition algorithm will tell you exactly which cards to review and when.
Start Free